“…Sequential pattern mining (SPM) (1,2), as an important knowledge discovery methods (3,4,5), focuses on finding interesting subsequences (called patterns) in sequences or sequence databases (SDBs). Various SPM methods have been investigated, such as SPM with gap constraints (6,7), high-utility SPM (8,9,10), contrast SPM (12,14,13,15), order-preserving SPM for time series (16), and closed SPM (17,18,19). However, most of these studies focuses on mining events (with each event corresponding to a character) that have occurred, which is called positive SPM (20,21).…”